Course: Grade 9 Applied Mathematics (MFM1P)
Unit 4:
Proportional Reasoning: Ratio, Rate and
Proportion
Unit 4
Proportional Reasoning: Ratio, Rate and Proportion
Section
4.1.2
4.1.3
4.1.4
4.1.J
4.2.1
4.2.2
4.2.J
4.3.1
4.3.2
4.3.P
4.4.1
4.4.2
4.4.3
4.4.4
4.4.P
4.5.1
4.5.2
4.5.P
4.5.J
4.6.2
4.6.P
4.W
4.S
4.R
4.RLS
Activity
Who Eats More? Worksheet
What’s in the Bag? Worksheet
Middle Mania (optional)
Journal Activity
Anticipation Guide
Growing Dilemma Investigation
Journal Activity
Television Viewing
Television Dimensions
Practice
Estimating Crowd Size
Techniques for Estimating Crowd Size
I’d Rather Be Scaling
More Scaling Problems
Practice
Elastic Meter and Percent
Types of Percent Problems
Practice
Journal Activity
Review Relay
Practice
Definitions
Unit Summary
Reflecting on My Learning (3, 2, 1)
Reflecting on Learning Skills
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4-2
4.1.2: Who Eats More? Worksheet
Task 1
Individually
Using the cards in Envelope 1:
a) Arrange them in order of which animal you believe eats more, from most to least.
Most
Least
In Pairs
b) Explain the reason why you placed the animals in this order.
Task 2
Pairs
Using the cards in Envelope 2:
a) Arrange them in order of which animal you believe eats more, from most to least.
Most
Least
b) Explain your reasons for this arrangement if it was different from the arrangement in Task 1.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
4-3
4.1.2: Who Eats More? Worksheet (continued)
Task 3
Pairs
Using the cards in Envelope 3:
a) Arrange them in order of which animal you believe eats more, from most to least.
Most
Least
b) Explain your reasons for this arrangement if it was different from the arrangement in Task 2.
Task 4
Groups of 4
a) Explain the reasoning used in Task 3.
Using the cards from Envelope 3:
b) Arrange them in a different order of which animal you believe eats more, by using the data
in another way.
Most
Least
c) Explain your reasons for this arrangement.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
4-4
4.1.2: Who Eats More? Worksheet (continued)
Task 5
Pairs
a) Compare the arrangements created in Task 3 and Task 4. Select the arrangement that you
believe best illustrates who eats more.
Task 3
Most
Least
Task 4
Most
Least
Justify your choice.
Task 6
Individually
a) Pick three other animals.
b) Predict their placement relative to the arrangement selected in Task 5.
Most
Least
c) Explain how you determined their placement.
d) Gather evidence to prove or disprove your prediction.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.1.3: What’s in the Bag? Worksheet
Station: What’s in the Bag?
At your station you have a bag with two different-coloured tiles.
1. Without looking, pull a tile out of the bag. Make a tally mark in the appropriate column in the
table below.
2. Put the tile back into the bag and shake it up.
3. Repeat steps 1 and 2 a total of 20 times.
Colour 1:
Colour 2:
Tally
Total
4. What appears to be the ratio of colour 1 to colour 2 in your bag?
5. Answer the following questions using the information you have collected.
Justify your answers.
a) If you had 30 of colour 1 in your bag, how many of colour 2 would you expect to have?
b) If you had 20 of colour 2 in your bag, how many of colour 1 would you expect to have?
c) If you had a total of 80 tiles in your bag, how many of each colour would you expect to
have?
d) If you had 40 of colour 1 in your bag, how many tiles in total would you expect to have?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
4-6
4.1.4: Middle Mania Worksheet - Optional
Station: GSP®4 Middle Mania
Launch GSP®4 Middle Mania on the computer and you should see the following. Follow
the instructions on the screen and complete the worksheet below.
Midpoint Trianlges
Midpoint Segments
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
4-7
4.1.4: Middle Mania Worksheet – Optional (continued)
1. Follow the Midpoint Triangle instructions and complete the following chart.
Area Δ ABC
24.98 cm²
Area Δ DEF
6.25 cm²
Ratio ABC/DEF
4.00:1
2. What do you notice about the ratio of the areas?
3. If Area ΔABC = 64 cm², what is the area of ΔDEF? Explain.
4. If Area ΔDEF = 15 cm², what is the area of ΔABC? Explain.
5. Follow the Midpoint Segments instructions and complete the following chart.
BC
DE
Ratio BC/DE
6. What do you notice about the ratio of the length of the line segments?
7. If the length of BC = 17 cm, what is the length of DE? Explain.
8. If length of DE = 22 cm, what is the length of BC? Explain.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
4-8
4.1.J: Journal Activity
List four examples of ratio, rate, and unit rate from your environment.
Example
Type
(Ratio, Rate, Unit Rate)
1.
2.
3.
4.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
4-9
4.2.1: Anticipation Guide
Instructions
•
Check Agree or Disagree, in ink, in the Before category beside each statement before you
start the Growing Dilemma task.
•
Compare your choice with your partner.
•
Revisit your choices at the end of the investigation.
Before
Agree
Disagree
Statement
After
Agree
Disagree
1. If you double the length of a square,
then the perimeter also doubles.
2. If you double the length of a square,
then the area also doubles.
3. If you double the length of a square,
then the length of the diagonal also
doubles.
4. If you double the sides of a cube, then
the volume also doubles.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.2.2: Growing Dilemma Investigation
Investigation 1: Perimeter Ratios
Use the colour tiles to create squares with the indicated side length.
1. Determine the perimeter for each side length.
2. Complete the chart.
3. Graph Perimeter vs. Side Length on the grid provided.
Side
Length
(S)
Perimeter
(P)
First
Differences
Ratio
(S:P)
Ratio in
Lowest
Terms
1
2
3
4
5
4. State the characteristics of this relationship:
a) first differences
b) ratios
c) graph
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.2.2: Growing Dilemma Investigation (continued)
Investigation 2: Area Ratios
Use the colour tiles to create squares with the indicated side length.
1. Determine the area for each side length.
2. Complete the chart.
3. Graph Area vs. Side Length on the grid provided.
Side
Length
(S)
Area
(A)
First
Differences
Ratio
(S:A)
Ratio in
Lowest
Terms
1
2
3
4
5
4. State 3 characteristics of this relationship:
a) first differences
b) ratios
c) graph
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.2.2: Growing Dilemma Investigation (continued)
Investigation 3: Diagonal Length Ratios
Use the colour tiles to create squares with the indicated side length.
1. Determine the length of the diagonal for each side length. Use Pythagorean Theorem.
a 2 + b2 = c 2
2. Complete the chart.
3. Graph Diagonal Length vs. Side Length on the grid provided.
Side
Length
(S)
Diagonal
(D)
First
Differences
Ratio
(S:D)
Ratio in
Lowest
Terms
1
2
3
4
5
4. State 3 characteristics of this relationship:
a) first differences
b) ratios
c) graph
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.2.2: Growing Dilemma Investigation (continued)
Investigation 4: Volume Ratios
Use the linking cubes or tiles to create cubes with the indicated side length.
1. Determine the volume of the cube for each side length.
2. Complete the chart.
3. Graph Volume vs. Side Length on the grid provided.
Side
Length
(S)
Volume
(V)
First
Differences
Ratio
(S:V)
Ratio in
Lowest
Terms
1
2
3
4
5
4. State 3 characteristics of this relationship:
a) first differences
b) ratios
c) graph
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.2.2: Growing Dilemma Investigation (continued)
A proportion is a statement of two equal ratios.
Conclusion
a) Which of the 4 relationships that you have investigated are proportional?
b) What else can you conclude about relationships that are proportional?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.2.J: Journal Activity
1. Give a personal example of proportional reasoning.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
2. Using the scenarios below, check for proportionality and justify your response.
(a)
You are paid an hourly wage. If you work 3 times the number of hours, does your
pay triple?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
(b)
Student council raffle tickets cost $0.50/each or 3 for $1. If you buy twice as many
tickets, does your cost double?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.3.1: Television Viewing
Use a different method to complete each part of the question.
You should be prepared to explain your methods to the class.
Did you know that there is an optimal distance for a person to be from a television for ideal
viewing?
The ratio of the size of the television screen to the distance a person should sit from it
is 1:6.
a) How far away should a person sit from a 20-inch television?
b) If the room is 17 feet long, can a person sit at an optimal distance from a 27-inch television?
Explain your reasoning.
c) What is the largest television that can be used in the 17-foot room for a person to sit an
optimal distance from it?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.3.2: Television Dimensions
3
Basic Television Information
4
•
Traditional televisions have a ratio of width to height of 4:3.
•
High definition televisions (HDTV) have a ratio of width to height of 16:9.
•
Television sizes are given as the length of the diagonal of the screen, i.e., a 27-inch
television is 27 inches from one corner to the diagonally opposite corner.
9
16
Problem 1
Darren wants to buy a new television. He finds a traditional television at the store and measures
the width of it to make sure it fits in his home. He measures the width to be 24 inches but he
forgets to measure the height and the diagonal.
a) Draw a diagram.
b) What is the height of the television?
c) What is the size of the television? (the length of the diagonal)
Problem 2
Sasha is buying a new HDTV. She finds one and measures the width to be about 35 inches.
a) Draw a diagram.
b) What is the height of the television?
b) What is the size of the television?
c) What is the optimal viewing distance for Sasha’s new HDTV?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.3.P: Practice
1. For safety reasons, a wheelchair ramp must be 1 m high for every 12 metres in
horizontal length.
The ratio of the height of the ramp to the length of the ramp is 1:12.
Draw a diagram.
(a) What is the horizontal length of a ramp that is 2 m tall?
(b) A ramp has a height of 2.6 m and a sloping length of 30 m. Is this wheelchair
ramp safe?
(c) Another wheel chair ramp is being built. It must be 4.8m in horizontal length.
Determine the sloping length of this new ramp.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.3.P: Practice (continued)
2. A ladder is leaning against a house. To be safe the ratio of the ladder’s length to the
distance of the ladder’s base from the house must be 5:3.
The ratio of the size of the ladder to the distance from the house is 5:3.
Draw a diagram.
(a) Determine how far the base of a 6.0 m ladder is from the house if it is being used
safely.
(b) How high up a wall does a 4.5 m ladder reach if it is being used safely?
(c) Is a 5.6m ladder is being used safely if its base is 3.3 m from the wall? Explain.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.1 Estimating Crowd Size
Exercise 1: Estimating the Size of a Crowd from an Aerial Diagram
Aerial Diagram of a political rally
1. Using the diagram above, choose a section to count the number of people; circle and
label this section. Complete the following table
Location (code)
Number of people
Total
2. How can you use the chart to estimate the total number of people at the rally?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.2 Techniques for Estimating Crowd Size
Caribou on Amethyst Island
Each year a fall caribou hunt is planned for Amethyst Island. It is important to determine how
many caribou live on the island before the Ministry of Natural Resources (MNR) issues hunting
licenses. The diagram below was made from the air of the herd on Amethyst Island. Determine
the number of caribou that are on Amethyst Island.
Scale :
Each square
represents 1km2
1. Find the total area of the grid above.
2. Complete the following chart by counting the caribou five boxes.
Location (code)
Number of caribou
Total
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.2 Techniques for Estimating Crowd Size (Continued)
total
3. a) Average number of caribou per square =
number of squares counted
b) Estimate the total number of caribou on the island.
Estimated number of caribou = average number of caribou per square x total number of squares
4. If the MNR has decided that one out of every six caribou can be hunted this year and each
hunter can only take one caribou, how many hunting licenses should be issued?
5. If the MNR has decided that 2 out of every 9 caribou can be hunted this year and each
hunter can only take one caribou, how many hunting licenses should be issued?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.2 Techniques for Estimating Crowd Size (Continued)
Manitouwadge Lake Sailing Regatta
A sailing regatta is a sailing competition. Competitive sailing is a sport with small teams of eight
per sailing vessel and boats 32-48 foot in length. After an initial sailing skills training, the teams
will sail their boats in a series of sprint training races to practice their skills in preparation for the
final regatta. Below is an aerial diagram of the Manitouwadge Lake Sailing Regatta.
Each small boat (no mast)
has two people on board.
Each large boat (with mast)
has six people on board.
1. Using the diagram complete the following chart.
Grid
Square
Number
Number of
small boats
# of people
on small
boats(2
people/boat)
Number of
large boats
# of people
on large
boats (6
people/boat)
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
total # of
people in
the grid
square
4-24
4.4.2 Techniques for Estimating Crowd Size (Continued)
1. What is the average number of people per grid square?
2. The Manitouwadge Lake Sailing Association charges $2.00 per person attending the
regatta. Based on the diagram how much money have they earned? Show your work.
3. The association is thinking of changing the fee to $5.00 per small boat and $10 per large
boat. If they made these changes for this year’s competition, how much could have been
earned? Show your work.
4. Should The Manitouwadge Lake Sailing Association base their fees per person or per boat?
Justify your answer.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.3: I'd Rather Be Scaling
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.4: More Scaling Problems
1. Dandelion Inquiry
In testing a new product for its effectiveness in killing dandelions,
it is necessary to find an area containing many dandelions,
count them, apply the product, and count the dandelions
again at a later time. How might this be accomplished
without counting every single dandelion? Design a
technique different from the one used in class.
2. Interpreting Scale Diagrams
Recall that scale = diagram measurement : actual measurement
Usa a ruler to measure the line.
a) Finding the scale
The actual length of this cell is 0.32 mm across.
What scale was used to draw this diagram?
b) Using the scale
This diagram was drawn using a scale of 1:7.
What is the actual height of this penguin?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.4: More Scaling Problems (continued)
3.
Complete the table.
i.
Scale
Diagram : Actual
1:400
ii.
12000:1
iii.
iv.
Diagram Measurement
6 cm
0.00375 mm
7.2 cm
1:250000
Actual Measurement
0.6 mm
8 cm
4.
The prices of a baseball glove and a tennis racket are in the ratio 7:12. If the price of the
racket is $62.40, determine the price of the glove.
5.
A particular mortar mix contains cement, water, and sand in the ratio 2:1:6. How much
cement and water should be in a batch of mortar containing 11.4 kg of sand?
6.
A picture of an ant is given below, determine the scale if its actual length is
2.4 mm
58 mm
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.4.P: Practice
1.
A Canadian football field is 110 yards long and 65 yards wide. Often the end zones
extend another 20 yards beyond the goal posts at each end of the field. Draw a scale
diagram of this playing field and the end zones using a scale of 1 square = 20 yards.
2.
The wheelbase of a vehicle is the distance between the front and back axles. Determine
the actual wheelbase of the vehicle in this scale drawing.
2.9 cm
Scale 1:50
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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elastic
4.5.1: Elastic Meter and Percent
Part A: Make the elastic meter
1. Take a piece of elastic 32 cm long. Mark a line at 1 cm from one end.
From this point make 10 marks every 3 cm. There will be 1 cm left.
(The centimetre at each end of the elastic provides a way to hold and stretch the
elastic ruler.)
2. On the first line write 10%; 2nd line, 20%; 3rd line, 30% (…up to 100%).
Part B: Use the elastic meter
3. Estimate from the bottom to the top where 60% of the right edge of your desk would be.
Put a very small pencil mark here. (Please erase it after the experiment.)
4. Stretch out the elastic meter from the bottom to the top, with 0% at the floor, and 100%
at the desk surface.
Use the 60% mark on the elastic meter to correct your estimate.
5. Use a measuring tape to measure this length. Record it in the appropriate place in the
following chart.
Percent %
0%
10%
33%
45%
50%
60%
75%
90%
100%
20%
10%
Measure (cm)
Use your elastic
meter to complete
the chart.
6. Graph your data on the grid below. Be sure to label your axes. Choose an appropriate scale.
7. On your graph draw a line of best fit.
Interpolate: Use line of best fit to estimate the lengths of the following percents:
a) 85%
b) 65%
c) 43%
d) 58%
Extrapolate: Estimate the following lengths:
a) 120%
b) 135%
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.5.2: Types of Percent Problems – Guided Lesson
1. Determining an unknown part:
a) Do together: HDTVs are on sale for 25% off. What is the discount on a television that
normally costs $885?
•
set up and solve a ratio
•
solve an equation 0.25 × 885 =
b) Do on your own: If you purchase a CD for $18.99, how much tax would you pay?
(both GST and PST)
2. Determining an unknown percent:
a) Do together: Shuva purchased a new MP3 player on sale. It was $219.50 originally, but
she paid $142.68, not including tax. What was the percent discount on the MP3 player?
•
set up and solve a ratio
•
solve an equation
× 219.50 = (219.50 – 142.68)
b) Do on your own: David was shopping for a new pair of shoes. He found a pair that was
$89.99 on sale for $22.50 off. What was the percent discount on the shoes?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.5.2: Types of Percent Problems – Guided Lesson (continued)
3. Determining the unknown whole:
a) Do together:
Cayla wanted to return a defective calculator, but her dog Buster had chewed up the
receipt. She could still see that the 13% tax came to $2.25. What was the cost of Cayla’s
calculator?
•
$2.25
set up and solve a ratio
•
b) Do on your own:
Himay was very happy because his new cell phone was on sale for 40% off and was
only $65.00. What was the original price of Himay’s phone?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.5.P: Practice
1.
2.
Express each of the following as a percent.
(a)
12 out of 16
(b)
one fifth
(c)
14
35
(d)
80:50
Find the number for each of the following.
(a)
3.
25% of a number is 5.
(b)
120% of a number is 48.
Find the amount for each of the following.
(a)
15% of 125g
(b)
9% of 45 cm
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.5.P: Practice (continued)
4.
5.
A skateboard is priced at $92.00 and is reduced by 20%.
(a)
What is the amount of the discount on the skateboard?
(b)
Calculate the new price of the skateboard.
In 2004, the cost to join a gym was $169.00.
In 2005, the cost was 7% more.
How much did it cost to join the gym in 2005?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.5.P: Practice (continued)
6.
On average, a girl will reach 90% of her final height by the time she is 11 years
old and 98% of her final height when she is 17 years old.
(a)
Beth is 11 years old. She is 150cm tall.
Estimate her height when she is 20 years old.
(b)
Lena is 17 years old. She is 176 cm tall.
Estimate her height when she is 30 years old.
(c)
Jodi is 35 years old. She is 165 cm tall.
(i)
Estimate her height at 11 years old.
(ii)
Estimate her height at 17 years old.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.5.J: Journal Activity
In the space provided, create your own percent reference sheet, showing examples of
the various types of percent problems.
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.6.2: Review Relay
1. Reduce the ratios to lowest terms:
2. Calculate the following percents:
15:35 =
45% of 220 =
18
=
6
120% × 555 =
1.5% × 1400 =
144:72 =
3. The driving distance from Thunder Bay to
Vancouver is approximately 2500 km.
How long would it take you to drive from
Thunder Bay to Vancouver at
90 km/hour without making any stops?
4. If the ratio of the Canadian dollar to the US
dollar is $1.04:$1.00, how much Canadian
money is equivalent to US$250?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.6.2: Review Relay (continued)
5. Measure the length indicated in
centimetres. What is the actual length of
the shark, in metres?
Scale Diagram
6. You want to purchase a new shirt that
costs $22.50.
a) How much tax will you have to pay
including GST and PST?
b) What is the total cost of your shirt?
1:70
7. You are shopping for DVDs at the video
store with a $30.00 gift certificate that you
received from a friend. You find a great
DVD that was $34.50 on sale for 25% off.
Do you have enough money to buy the
DVD including GST and PST?
8. You are working at Tecky Television
Sales. Recall that the HDTV’s width:height
ratio is 16:9. A customer wants to know:
a) If he has an entertainment centre that
has an opening that is 48 inches wide,
how high will the cabinet opening have
to be?
b) If the cabinet opening is 48 inches by
32 inches, will a 50-inch HDTV fit
inside?
MFM 1P - Grade 9 Applied Mathematics – Unit 4: Proportional Reasoning (DPCDSB Dec 2008)
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4.6.P: Practice
1.
Express each of the following as a unit rate. Round answers to two decimal
places, if necessary, and state the units for each answer.
(a)
40 mm of rain in 4 h ______________________________
(b)
$6.49 for 24 cans of pop ___________________________
(c)
$58.00 for 8 h of work _____________________________
2.
A newborn child usually triples its birth weight in a year. If a baby weighed 3.35 kg
at birth, what is the baby likely to weigh on her first birthday?
3.
A single bus fare costs $2.10. A monthly bus pass costs $50.00. Katelyn estimates
that she will ride the bus 25 times this month. Boris estimates that he will ride the
bus 16 times. Should they each buy a monthly pass? Explain.
4.
The price for gold is usually given in US dollars per ounce. Find the cost in
Canadian dollars for an ounce of gold selling at US$559.00 when the exchange
rate is $1 USD = $1.17 CDN.
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4.6.P: Practice (continued)
5.
Determine the better buy for each of these school supplies. Show your calculations.
(a) A box of 12 pens for $2.59 or a box of 15 pens for $3.35.
(b) 250 sheets of graph paper for $2.39 or 120 sheets for $1.15.
6. Kelly ran 8 laps of the track in 18 minutes. Jack ran 6 laps in 10 minutes. Who had the
greater average speed? Explain.
7.
Carl bought a football jersey with a regular price of $129.49. The jersey was on
sale for 30% off, and the taxes were 14%. Determine each amount.
(a)
the discount
(b)
the sale price
(c)
the taxes
(d)
the total amount Carl paid
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4.6.P: Practice (continued)
8.
9.
Determine the missing value for each of the following.
(a)
64 = ______%
72
(b)
15% of _______ = 6
(c)
32% of 65 = ______
(d)
0.08% of 25 000 000 = ________
(e)
124 = ______%
96
(f)
135% of _____ is 108.
10. A stop sign has an actual width of 60 cm. Determine the scale of the diagram
below.
3.6 cm
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4.6.P: Practice (continued)
11. The Canadian Flag has a width to height ratio of 2:1. On a 1:50 scale
drawing of a flag its width is 13.0 cm. What is the actual size of this flag?
Actual height:__________
Actual width:_____________
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4.W: Definition Page
Term
Picture / Sketch /
Examples
Definition
Algebraic Reasoning
Constant of Proportionality
Cross Product
Equivalent Ratios
Fraction
Lowest Terms
Percent
Probability
Qualitative
Quantitative
Rate
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4.W: Definition Page (continued)
Term
Picture / Sketch /
Examples
Definition
Ratio
Scale
Scale Diagram
Scaling
Unit Price
Unit Rate
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4.S: Unit Summary Page
Rate
Percent
Ratio
Complete the concepts circles for Rate, Ratio and Percent.
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4.R: Reflecting on My Learning (3, 2, 1)
3 Things I know well from this unit
2 Things I need explained more
1 Question I still have
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4.RLS: Reflecting on Learning Skills
Students should be aware of the importance that these skills have on your performance.
After receiving your marked assessment, answer the following questions. Be honest
with yourself. Good Learning Skills will help you now, in other courses and in the future.
E – Always
G – Sometimes
S – Need Improvement
N – Never
Organization
E G S N
E G S N
E G S N
I came prepared for class with all materials
My work is submitted on time
I keep my notebook organized.
Work Habits
E G S N
E G S N
E G S N
E G S N
E G S N
E G S N
I attempt all of my homework
I use my class time efficiently
I limit my talking to the math topic on hand
I am on time
If I am away, I ask someone what I missed,
I complete the work from the day that I missed.
Team Work
E G S N
E G S N
E G S N
I am an active participant in pairs/group work
I co-operate with others within my group
I respect the opinions of others
Initiative
E G S
E G S
E G S
E G S
I participate in class discussion/lessons
When I have difficulty I seek extra help
After I resolve my difficulties, I reattempt the problem
I review the daily lesson/ideas/concepts
N
N
N
N
Works Independently
E G S N
I attempt the work on my own
E G S N
I try before seeking help
E G S N
If I have difficulties I ask others but I stay on task
E G S N
I am committed to tasks at hand
Yes No
I know all the different ways available in my school, where I can seek extra help.
Yes No
I tried my best.
What will I do differently in the next unit to improve?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
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